A discrete unified gas kinetic scheme with sparse velocity grid for rarefied gas flows

In this paper, a discrete unified gas kinetic scheme (DUGKS) with a sparse grid method applied in velocity space (DUGKS-SG) is proposed for simulating rarefied gas flows. The DUGKS-SG decomposes the computationally demanding problem into smaller and independent subproblems, thereby reducing the computational costs and exhibiting good parallelism. Several numerical tests, including the two-dimensional Riemann problem and the lid-driven microcavity flow, have been conducted to validate the performance of the DUGKS-SG. Comparisons with the original DUGKS and the Direct Simulation Monte Carlo (DSMC) method demonstrate that DUGKS-SG can provide satisfactory results with improved efficiency. Specifically, a maximum speedup of 9.486 for a 2D case with 7 CPU cores and 13.035 for a 3D case with 8 CPU cores can be achieved. These results suggest that the proposed DUGKS-SG can serve as an efficient numerical method for rarefied gas flow simulations. •A DUGKS with sparse velocity grid is proposed for simulating rarefied gas flows.•Present method reduces computational costs and maintains accuracy of original DUGKS.•The present method exhibits good parallelism.